Magnetic field components are measured at multiple longitudinal positions and used to calculate estimated longitudinal position and length of a transversely localized electric current segment flowing across a gap between conductive bodies. The apparatus can be used with a remelting furnace. The electrode and ingot act as the conductive bodies, and arcs, discharges, or slag currents are the current segments spanning the gap. Actuators for movable sensors can be coupled to the sensors in a servomechanism arrangement to move the sensors along with the moving gap. An actuator for moving one of the conductive bodies can be coupled to sensors in a servomechanism arrangement to maintain the gap distance within a selected range as the gap moves.